Bifurcation for the solutions of equations involving set valued mappings

Variational-Like Inclusions and Resolvent Equations Involving Infinite Family of Set-Valued Mappings

A Sard Theorem for Set-Valued Mappings∗†

If F is a set-valued mapping from IRn into IRm with closed graph, then y ∈ IRm is a critical value of F if for some x with y ∈ F (x), F is not metrically regular at (x, y). We prove that the set of critical values of a set-valued mapping whose graph is a definable (tame) set in an o-minimal structure containing additions and multiplications is a set of dimension not greater than m − 1 (resp. a ...

Fixed Point Theorems for Set-valued Mappings

Characterization of weak fixed point property for new class of set-valued nonexpansive mappings

In this paper, we introduce a new class of set-valued mappings which is called MD-type mappings. This class of mappings is a set-valued case of a class of the D-type mappings. The class of D-type mappings is a generalization of nonexpansive mappings that recently introduced by Kaewkhao and Sokhuma. The class of MD-type mappings includes upper semi-continuous Suzuki type mappings, upper semi-con...

Approximate Solutions of Set-Valued Stochastic Differential Equations

In this paper, we consider the problem of approximate solutions of set-valued stochastic differential equations. We firstly prove an inequality of set-valued Itô integrals, which is related to classical Itô isometry, and an inequality of set-valued Lebesgue integrals. Both of the inequalities play an important role to discuss set-valued stochastic differential equations. Then we mainly state th...